Elementary-base cirquent calculus I: Parallel and choice connectives
arXiv:1707.04823
Abstract
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the game-semantically conceived logic of computational problems - see http://www.csc.villanova.edu/~japaridz/CL/ ) whose logical vocabulary consists of negation and parallel and choice connectives, and whose atoms represent elementary, i.e. moveless, games.
References in corpus (15)
- Sequential operators in computability logic
- Introduction to Cirquent Calculus and Abstract Resource Semantics
- Propositional computability logic I
- Cirquent calculus deepened
- From truth to computability I
- The intuitionistic fragment of computability logic at the propositional level
- Many concepts and two logics of algorithmic reduction
- The taming of recurrences in computability logic through cirquent calculus, Part I
- Toggling operators in computability logic
- From formulas to cirquents in computability logic
- The parallel versus branching recurrences in computability logic
- A logical basis for constructive systems
- On the system CL12 of computability logic
- Separating the basic logics of the basic recurrences
- The Computational Complexity of Propositional Cirquent Calculus